Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices

Extensive Monte Carlo simulations were performed to study bond percolation on the simple cubic (sc), face-centered-cubic (fee), and body-centered-cubic (bcc) lattices, using an epidemic approach. These simulations provide very precise values of the critical thresholds for each of the lattices: p(c)(sc) = 0.2488126+/-0.0000005, p(c)(fcc) = 0.1201635+/-0.0000010, and p(c)(bcc) = 0.1802875+/-0.0000010. For p close to p(c), the results follow the expected finite-size and scaling behavior, with values for the Fisher exponent tau (2.189+/-0.002), the finite-size correction exponent Omega (0.64+/-0.02), and the scaling function exponent sigma (0.445+/-0.01) confirmed to be universal.